Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80

Marilyn Cameron
2022-10-24
Answered

Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80

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scranna0o

Answered 2022-10-25
Author has **16** answers

The general term of a Geometric Sequence is given by

$a}_{n}=a\cdot {r}^{n-1$

Where a is the first term also known as $a}_{1$ and r is the common ratio.

We have $a}_{1$ if we get r we can easily find $a}_{19$ by using 19 for n

Let us start by writing the given term using r

$a}_{9}=a\cdot {r}^{8$

If we divide $a}_{9$ by $a}_{1$ we would get an equation in r

$\frac{a{r}^{8}}{a}=\frac{358.80}{14}$

${r}^{8}=25.628571428571428571428571428571$

Taking 8th root.

$r=\sqrt[8]{25.628571428571428571428571428571}$

#r=1.4999975504465127405341330547934"

$r\approx 1.5$

$a}_{19}=14{\left(1.5\right)}^{19$

$a}_{19}=31,035.729480743408203125\text{$

${a}_{19}\approx 31035.73$

$a}_{n}=a\cdot {r}^{n-1$

Where a is the first term also known as $a}_{1$ and r is the common ratio.

We have $a}_{1$ if we get r we can easily find $a}_{19$ by using 19 for n

Let us start by writing the given term using r

$a}_{9}=a\cdot {r}^{8$

If we divide $a}_{9$ by $a}_{1$ we would get an equation in r

$\frac{a{r}^{8}}{a}=\frac{358.80}{14}$

${r}^{8}=25.628571428571428571428571428571$

Taking 8th root.

$r=\sqrt[8]{25.628571428571428571428571428571}$

#r=1.4999975504465127405341330547934"

$r\approx 1.5$

$a}_{19}=14{\left(1.5\right)}^{19$

$a}_{19}=31,035.729480743408203125\text{$

${a}_{19}\approx 31035.73$

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